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Sampling error. Differences between the characteristics of the sample and the population Decreases as size of sample increases Rule of thumb: number of cases in the smallest group or subgroup to be separately measured, tested or compared should be at least 30 . Representative sampling. Selecting
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1. Sampling Population: Every member, “case” or element of the group to which your findings are intended to apply
Sampling frame: A list that contains each element
Sample: A subset of “cases” or elements selected from a population
Why do we sample?
To describe characteristics of a population, or test a hypotheses when measuring each case is too expensive or impractical
To test a hypotheses using inferential (probability) statistics
2. Sampling error Differences between the characteristics of the sample and the population
Decreases as size of sample increases
Rule of thumb: number of cases in the smallest group or subgroup to be separately measured, tested or compared should be at least 30
3. Representative sampling Selecting members so that characteristics of the sample accurately reflect the characteristics of the population
Purpose: To be able to generalize from the sample to the population
Limitation: Can only generalize to the population from which the sample was drawn
4. Probability sampling Each element or “case” in the population has an equal chance to be selected and become a part of the sample.
If the sampling frame is 5 and we draw two from a hat, each element’s probability of being selected is 2/5 (.20) on the first draw.
Sampling with replacement: During selection, drawn elements are returned to the population. This keeps the probability of any element being drawn the same but makes duplicate draws possible.
On the second draw, each remaining element’s probability of being drawn is 1/5 (.20).
5. Sampling without replacement: During selection, drawn elements are not returned to the population
On the second draw, each remaining element’s probability of being drawn is ¼ (.25).
Sampling without replacement is most common since most sampling frames are sufficiently large so that as elements are drawn, changes in probability are small
6. Probability sampling techniques Simple random sampling: Each element and combination of elements has the same chance of being selectedBring out the chips!
10. Stratified random sampling: Divide population into categories (strata) and randomly sample within each
Proportionate: Number of elements in each category is proportionate to that category’s representation in the population.
12. Disproportionate sampling: Randomly drawing a disproportionate number of elements from a specific strata whose overall representation is low.
14. Sampling exercise, Sin City Research question: Is there more likely to be a personal relationship between suspect and victim in violent crimes or in crimes against property?
You have full access to crime data for “Sin City” in 2004. These statistics show there were 200 crimes, of which 75 percent were property crimes and 25 percent were violent crimes. For each crime, you know whether the victim and the suspect were acquainted (yes/no).
1. Identify the population.
2. How would you sample?
3. Would you stratify? How?
4. Do it two ways – using proportionate and disproportionate techniques. Which is better? Why?
17. Jay’s cynicism reduction program Hypothesis: Training reduces cynicism
The Anywhere Police Department has 200 patrol officers, of which 150 are males and 50 are females. Jay wants to conduct an experiment using control groups to test his program.
1. Identify the population.
2. How would you sample?
3. Would you stratify? How?
4. Is it better to use proportionate or disproportionate techniques. Why?
19. Systematic sampling: Randomly select first element, then choose every 5th, 10th, etc. depending on the size of the frame.
Problem: Sampling list that is ordered in a particular way could result in a non-representative sample
Cluster sampling: Divide population into equal-sized groups (clusters) chosen on the basis of a neutral characteristic, then draw a random sample of clusters. The study sample contains every element of the chosen clusters.
Often done to study public opinion (city divided into blocks)
Rule of equally-sized clusters usually violated
The “neutral” characteristic may wind up being an extraneous variable and affect outcomes!
Since not everyone in the population has an equal chance of being selected, there will be sampling error Quasi-probability sampling
20. Nonprobability sampling Accidental sample: Subjects who happen to be encountered by researchers
Example – observer ridealongs in police cars
Quota sample: Elements are included in proportion to their known representation in the population
Purposive/“convenience” sample: Researcher uses best judgment to select elements that typify the population
Example: Interview all burglars arrested during the past month